1. Max-Planck-Institut für Plasmaphysik, EURATOM Association Computational Plasmaphysics Ralf Schneider Max-Planck-Institut für Plasmaphysik, Euratom-IPP Association, Wendelsteinstra  e 1, D-17491 Greifswald, Germany

2. Max-Planck-Institut für Plasmaphysik, EURATOM Association Computational physics Why numerical methods? Complexity of equations Example Simulation of experiments To test validity of theory To gain an idea of experimental performance

3. Max-Planck-Institut für Plasmaphysik, EURATOM Association Computational physics

4. The Computational Stellarator W7-X Max-Planck-Institut für Plasmaphysik, EURATOM Association

8. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma Wendelstein 7-X

9. slow drift of guiding center Max-Planck-Institut für Plasmaphysik, EURATOM Association

10. Optimized stellarator

11. Plasma in a computational model 10 Variables: densities, velocities, temperatures 10 billion grid points 100 million time steps 100 FL oating P oint OP erations /sec / timestep / gridpoint or 1 billion teraflop/sec Cray T3E with 784 PE (ca. 75 gigaflop) or 500 years computing NOT VERY REALISTIC Max-Planck-Institut für Plasmaphysik, EURATOM Association

12. Plasma: Max-Planck-Institut für Plasmaphysik, EURATOM Association

13. Particle aspect of plasma dominates Max-Planck-Institut für Plasmaphysik, EURATOM Association

14. Plasma is treated as one fluid with infinite conductivity Max-Planck-Institut für Plasmaphysik, EURATOM Association

16. MHD is basis for all equilibrium calculations

17. Max-Planck-Institut für Plasmaphysik, EURATOM Association

18. Existence in 3D ? Theoretical ? Experimental ? Accessible only by computational models but not before 1975 thus Optimization started with IBM360/91 W7-AS Design 1978 Max-Planck-Institut für Plasmaphysik, EURATOM Association MHD, equilibrium

19. p constant on (nested) surfaces labelled by s Poloidal and toroidal fluxes are invariant functions, together with m(s) the mass distribution Stationary states of plasma energy (fixed boundary) MHD force balance r and z periodic functions ( Fourier series) Hybrid finite elements in s, (artificial) Time-like iteration Max-Planck-Institut für Plasmaphysik, EURATOM Association Equilibria, VMEC

20. Max-Planck-Institut für Plasmaphysik, EURATOM Association

21. NESTOR / NESCOIL codes Iterative combination of VMEC & NESCOIL allows free-boundary computations NEMEC Max-Planck-Institut für Plasmaphysik, EURATOM Association Vacuum fields - free-boundary - coils Boundary Value Problems, Greens Function Last closed magnetic surface (lcms) defines completely interior plasma properties Search for external current distributions (i.e. coils) producing a vacuum field B with boundary conditions on the lcms (n exterior normal)

22. Max-Planck-Institut für Plasmaphysik, EURATOM Association VMEC

23. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma configuration given calculate coils to produce it

24. Max-Planck-Institut für Plasmaphysik, EURATOM Association Coils 1-50

25. Max-Planck-Institut für Plasmaphysik, EURATOM Association Is a given plasma configuration stable against small pertubations? Find ways to prevent instabilities

26. Max-Planck-Institut für Plasmaphysik, EURATOM Association Tokamak operation limited by MHD instabilities

27. Max-Planck-Institut für Plasmaphysik, EURATOM Association

28. Necessary to design equilibrium with „good“ confinement properties

29. Max-Planck-Institut für Plasmaphysik, EURATOM Association

31. Speedup of equilibrium codes due to Peak speed of cpu: 10 fold IBM 360/91 Cray-1S 1980 (same parameters) 12 fold Cray-1S YMP-464(4cpus) 1988 16 fold Cray-1S J916 (16) 1992 28 fold Cray-1S SX4(2) 1996 500 fold Cray-1S T3E-600(784) 1998 New Codes: 24 fold BETA MOMCON/FIT 1980 (same equilibrium) 50 fold MOMCON VMEC 1985 30 fold VMEC VMEC2 1989 Better algorithms gave a speedup of around 30.000 ! New hardware ``only`` 5.000... Max-Planck-Institut für Plasmaphysik, EURATOM Association Computational Remarks

32. Max-Planck-Institut für Plasmaphysik, EURATOM Association Turbulence suppression

33. Max-Planck-Institut für Plasmaphysik, EURATOM Association Turbulence suppression

39. Max-Planck-Institut für Plasmaphysik, EURATOM Association Gyrokinetic turbulence simulations

44. Max-Planck-Institut für Plasmaphysik, EURATOM Association Plasma-edge physics

45. Max-Planck-Institut für Plasmaphysik, EURATOM Association Length scales sputtered and backscattered species and fluxes Plasma-wall interaction Molecular dynamics Binary collision approximation Kinetic Monte Carlo Kinetic model Fluid model impinging particle and energy fluxes

46. Carbon deposition in divertor regions of JET and ASDEX UPGRADE JET ASDEX UPGRADE ASDEX UPGRADE Achim von Keudell (IPP, Garching) V. Rohde (IPP, Garching) Paul Coad (JET) Major topics: tritium codeposition chemical erosion Max-Planck-Institut für Plasmaphysik, EURATOM Association Diffusion in graphite

47. Max-Planck-Institut für Plasmaphysik, EURATOM Association Diffusion in graphite Internal Structure of Graphite Granule sizes ~ microns Void sizes ~ 0.1 microns Crystallite sizes ~ 50-100 Ångstroms Micro-void sizes ~ 5-10 Ångstroms Multi-scale problem in space (1cm to Ångstroms) and time (pico-seconds to seconds)

48. Max-Planck-Institut für Plasmaphysik, EURATOM Association Multi-scale ansatz Mikroscales MC Mesoscales KMC Macroscales KMC and Monte Carlo Diffusion (MCD)

49. Max-Planck-Institut für Plasmaphysik, EURATOM Association Molecular dynamics – HCParcas code Developed by Kai Nordlund, Accelarator laboratory, University of Helsinki - Hydrogen in perfect crystal graphite – 960 atoms - Brenner potential, Nordlund range interaction - Berendsen thermostat, 150K to 900K for 100ps - Periodic boundary conditions

50. Equilibration of pressure with time Max-Planck-Institut für Plasmaphysik, EURATOM Association Time variation of pressure

51. Max-Planck-Institut für Plasmaphysik, EURATOM Association Molecular dynamics – Simulation at 150K, 900K 150K 900K

52. Max-Planck-Institut für Plasmaphysik, EURATOM Association Molecular dynamics results two diffusion channels no diffusion across graphene layers (150K – 900K) Lévy flights?

53. Non-Arrhenius temperature dependence Max-Planck-Institut für Plasmaphysik, EURATOM Association Molecular dynamic results

54. Max-Planck-Institut für Plasmaphysik, EURATOM Association Kinetic Monte Carlo – basic idea  0 = jump attempt frequency (s -1 ) E m = migration energy (eV) T = trapped species temperature (K) Assumptions: - Poisson process (assigns real time to the jumps) - jumps are not correlated

55. Max-Planck-Institut für Plasmaphysik, EURATOM Association KMC results for transgranular diffusion - strong dependence on void sizes and not on void fraction - saturated H (Tanabe)  0 ~10 5 s -1 and step sizes ~1Å (QM?)

56. Max-Planck-Institut für Plasmaphysik, EURATOM Association Multiscale model Activation energies: trapping-detrapping 2.7 eV desorption 1.9 eV surface diffusion 0.9 eV, jump attempt frequency, jump step length for entering the surface for a solute H atom 2.7 eV  0 ~10 13 s -1 ~35Å porous graphite structure

57. desorption starts between 900 K and 1200 K Max-Planck-Institut für Plasmaphysik, EURATOM Association Multiscale model - results

58. Max-Planck-Institut für Plasmaphysik, EURATOM Association Multiscale model – 900 K, 0.1 ms

59. Max-Planck-Institut für Plasmaphysik, EURATOM Association Multiscale model – 1500 K, 0.001 ms

60. Max-Planck-Institut für Plasmaphysik, EURATOM Association Multiscale model – diffusion types adsorption- desorption 1.9 eV surface diffusion 0.9 eV

61. Applications: Low temperature plasmas (methane, RF discharges) Complex plasmas (plasma crystals) Parasitic plasmas in the divertor (radiative ionization) Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC(Particle-in-cell)-method Principle:

62. n e ~ 10 9 -10 10 cm -3 n n ~ 10 15 -10 16 cm -3 f RF = 13.56 MHz potential n e = 10 10 cm -3, n H 2 = 9.2·10 14 cm -3, n CH 4 = 7·10 14 cm -3, p = 0.085 Torr (11 Pa) Model system for chemical sputtering: methane plasma (2DX3DV PICMCC multispecies) Collaboration with IEP5, Bochum University (Ivonne Möller) Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC simulation: RF capacitive discharge

63. CH 4 + ion energy distribution electron and CH 4 + ion density Electrons reach electrode only during sheaths collapse Energetic ions at the wall due to acceleration in the sheath Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC simulation: RF capacitive discharge

64. Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC simulation: RF capacitive discharge electron velocity distributionelectron-impact ionization rate Energetic electrons oscillate between sheaths Ionization spread over the bulk

65. Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC simulation: RF capacitive discharge electron energy probability function Figure from V.A. Godyak, et al., Phys. Rev. Lett., 65 (1990) 996. Bi-maxwellian distribution due to stochastic heating

66. Lower electrode Negative charge due to higher electron mobility Levitation in strong sheath electric field Max-Planck-Institut für Plasmaphysik, EURATOM Association Dusty (complex) plasmas

67. Max-Planck-Institut für Plasmaphysik, EURATOM Association PIC simulation: Plasma crystal - full 3D! Quasi - ordered 3D structure Top view

68. Complex multi-scale physics requires complex computational tools Max-Planck-Institut für Plasmaphysik, EURATOM Association

69. Thanks!! Ralf Kleiber, Ulrich Schwenn, Volodja Kornilov, Stefan Sorge Mathias Borchardt, Jörg Riemann, Alex Runov, Xavier Bonnin Konstantin Matyash, Neil McTaggart, Manoj Warrier, Francesco Taccogna Andrea Pulss, Andreas Mutzke, Henry Leyh And many contributions from colleagues all over the world